Definite Integrals in AP Calculus AB/BC

Definition

Definite integrals are used to find the exact value of the area under a curve between two points on the x-axis. It represents the accumulation of infinitesimally small areas and can be thought of as finding the total "signed" area.

Related terms

Antiderivatives:

Antiderivatives are functions that "undo" derivatives. They represent families of functions that have the same derivative.

Riemann Sums: Riemann sums are approximations of definite integrals by dividing an interval into smaller subintervals and summing up areas using rectangles or trapezoids.

Fundamental Theorem of Calculus:

The fundamental theorem of calculus establishes a connection between definite integrals and antiderivatives, stating that if F(x) is an antiderivative of f(x), then ∫[a,b] f(x) dx = F(b) - F(a).